Big Table of Possibilities (Proton Resonances)

Proton and Delta Resonance Transitions in Quantized Superfluid Model

n	J	Predicted Energy (MeV)	Possible Match	Measured Mass (MeV)	Match Quality
4	1/2	938	N(938) P11	939	Exact
4	3/2	1232	Δ(1232) P33	1232	Exact
4	5/2	1722	N(1680) F15	1685	Close
4	7/2	2408	N(2250) G19	2250	Tentative (J mismatch)
5	1/2	1440	N(1440) P11	1440	Exact
5	3/2	1734	N(1720) P13	1720	Close
5	5/2	2224	N(2220) H19	2220	Tentative (J mismatch)
5	7/2	2910	None	-	None
6	1/2	1710	N(1710) P11	1710	Exact
6	3/2	2004	Δ(1950) F37	1950	Tentative (J mismatch)
6	5/2	2494	Possible higher resonances	-	Tentative
6	7/2	3180	None	-	None
7	1/2	1748	N(1880) or Δ(1900)	~1880 or ~1900	Tentative
7	3/2	2042	N(2000) or Δ(2000)	~2000	Tentative
7	5/2	2532	Possible higher resonances	-	Tentative
7	7/2	3218	None	-	None

Notes: Predicted energies are calculated using \( E_{n,J} = E_n + [J(J+1) - \frac{3}{4}] \times 98 \) MeV, where \( E_n = -3390 + 1546n - 116n^2 \) MeV for \( J = \frac{1}{2} \). The total energy includes the proton rest mass (938 MeV) at the ground state (\( n = 4, J = \frac{1}{2} \)). Match quality reflects proximity to measured masses and consistency with quantum numbers (J, parity, etc.). For \( n > 7 \), the quadratic formula predicts decreasing energies (e.g., \( n = 8, E_n = 1554 \) MeV), which may not be physical, so the table is limited to \( n = 4 \) to \( n = 7 \).

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